Understanding the permutation notation of P(n, n-1).

What does P(n, n-1) mean?

Working with some identical objects using permutations and combinations.

Wing has different books to arrange on a shelf: 4 blue, 3 green, and 2 red. (a) In how many ways can the books be arranged on a shelf? (b) If books of the same color are to be grouped together, how many arrangements are possible? (c) In how many distinguishable ways can the books be arranged if books of the same color are identical but need not be grouped together? (d) In how many ways can you select 3 books, one of each color, if the order in which the books are selected does not matter?

Combinations

Five cards are chosen from an ordinary deck to form a hand in poker. In how many ways is it possible to get the following results? (a) 4 queens (b) no face card (c) exactly 2 face cards (d) 1 heart, 2 diamonds, and 2 clubs

Working with combinations to select a baseball team.

The coach of the Morton Valley Softball Team has 6 good hitters and 8 poor hitters. He chooses 3 hitters at random. (a) In how many ways can he choose 2 good hitters and 1 poor hitter? (b) In how many ways can he choose 3 good hitters? (c) In how many ways can he choose at least 2 good hitters?

Finding the probability of various bridge hands.

A bridge hand is made up of 13 cards from a deck of 52. Find the probability that a hand chosen at random contains the following. (A) Only hearts (B) Exactly 3 aces and exactly 3 kings